Simulations of Subtropical Cyclones in a Baroclinic ...as having some characteristics of extratropical and trop-ical cyclones simultaneously. As noted by Evans and Guishard (2009)

Simulations of Subtropical Cyclones in a Baroclinic Channel Model

CHRISTOPHER A. DAVIS

National Center for Atmospheric Research,* Boulder, Colorado

(Manuscript received 14 December 2009, in final form 4 May 2010)

ABSTRACT

The present study considers a variety of cyclone developments that occur in an idealized, baroclinic channel

model featuring full condensation heating effects over an ocean with prescribed sea surface temperature

variation. The geostrophic basic-state jet is specified by the tropopause shape, and horizontal shear is included

by specifying the meridional variation of zonal wind on the lower boundary. The horizontal shear induces

anticyclonic wave breaking of baroclinic waves. Normal mode perturbations are computed using a ‘‘fake-dry’’

version of the model but integrated forward using full physics.

Low-latitude moist convection is particularly strong in simulations with strong surface easterlies that de-

stabilize the troposphere through water vapor fluxes from the ocean surface. Deep convection produces

a locally elevated dynamic tropopause and an associated anticyclone. This modified zonal flow supports moist

baroclinic instability. The resulting cyclones, identified as subtropical cyclones, occur in deep westerly vertical

wind shear but are nearly devoid of lower-tropospheric baroclinicity initially. These systems are distinguished

from baroclinically dominated secondary cyclones that also form at relatively low latitudes in the simulations.

For weak jets and strong subtropical surface easterlies, subtropical cyclone development dominates for-

mation on the midlatitude jet. For strong westerly jets or weak horizontal shear, the situation is reversed and

the midlatitude baroclinic wave can help or hinder the ultimate intensification of the subtropical cyclone. The

similarity of this cross-latitude influence to the extratropical transition of tropical cyclones is noted.

1. Introduction

What are subtropical cyclones? Cyclones forming in

the subtropics, roughly 23–358 from the equator, have

long presented challenges for basic understanding,

classification, and forecasting. They have been regarded

as having some characteristics of extratropical and trop-

ical cyclones simultaneously. As noted by Evans and

Guishard (2009) and Guishard et al. (2009), they are in-

consistently included in the database for tropical cy-

clones. Their distinction from conventional extratropical

cyclones is subtle. Cyclone phase space (CPS) diagrams

(Hart 2003) suggest that these disturbances develop in

baroclinic environments but that the baroclinicity is

relatively shallow and weak compared to that in cool

season midlatitude cyclones. Furthermore, deep moist

convection is thought to influence subtropical cyclones

fundamentally, yet this contribution has not been

quantified.

To set the context for a study of subtropical cy-

clones, the dependence of the life cycle of cyclones on

condensation heating, baroclinicity, and meridional

shear of the zonal wind is first reviewed. Idealized

baroclinic wave simulations have revealed the exis-

tence of a variety of cyclone types even without the

condensation process. Davies et al. (1991), Thorncroft

et al. (1993), and Wernli et al. (1998) identified distinct

paradigms of cyclone development depending on the

sign and strength of the barotropic shear added to

a midlatitude jet. The Rossby waves exhibited wave

breaking that mirrored the sense of the shear. Cy-

clonic wave breaking in cyclonic barotropic shear

resulted in large, deep cyclones. Anticyclonic wave

breaking in anticyclonic shear resulted in strong anti-

cyclones and anticyclonically curved filaments of po-

tential vorticity (PV) in the upper troposphere. This

picture has been clarified and modified somewhat in

more recent work by Orlanski (2003), who emphasized

the importance of surface baroclinicity and the intensity

* The National Center for Atmospheric Research is sponsored

by the National Science Foundation.

Corresponding author address: Christopher A. Davis, P.O. Box

3000, Boulder, CO 80307.

E-mail: [email protected]

SEPTEMBER 2010 D A V I S 2871

DOI: 10.1175/2010JAS3411.1

� 2010 American Meteorological Society

of surface cyclone development in determining whether

waves break cyclonically or anticyclonically. Still, the

basic paradigm of wave-breaking dichotomy has en-

joyed considerable utility.

A curious result of simulations in anticyclonic shear is

the appearance of secondary cyclone formation where

the end of the upper-tropospheric PV filament, having

amalgamated into a closed low, approaches a surface

baroclinic zone (Simmons and Hoskins 1978; Thorncroft

and Hoskins 1990). This secondary cyclone occurs far to

the south of the primary cyclone growing on the mid-

latitude jet. The real-world counterpart of this type of

cyclone is probably the kona low (Daingerfield 1921;

Simpson 1952; Otkin and Martin 2004) and cyclones

with similar evolution that occur at other longitudes.

Occasionally these cyclones become tropical cyclones

(Davis and Bosart 2003). The basic dynamics of these

cyclones, at least initially, is still baroclinic. Cyclones

like these are often termed subtropical cyclones because

of the latitude range in which they occur.

The addition of moisture introduces considerable com-

plexity to the cyclone problem even in the context of

idealized simulations. It is well known that condensation

heating can destabilize short length scales with respect

to adiabatic baroclinic instability (Whitaker and Davis

1994). In fact, the growth rate of disturbances becomes

relatively independent of wavelength with condensation

heating (exactly so in the two-dimensional case). Con-

densation decreases the horizontal length scale of ordi-

nary baroclinic waves (Emanuel et al. 1987). It also gives

rise to entirely new phenomena such as diabatic Rossby

waves (Parker and Thorpe 1995; Wernli et al. 2002) and

diabatic Rossby vortices (DRVs; Moore and Montgomery

2005). The latter form in the presence of strong conden-

sation heating and modest vertical wind shear. A close

cousin of the DRV is the mesoscale convective vortex

(MCV) that forms from organized mesoscale convection,

and through baroclinic processes may engender and or-

ganize new convection (Raymond and Jiang 1990). As

may be inferred from Conzemius et al. (2007), there is

a duality between coherent vortices emerging from or-

ganized convection and the development of cyclones with

relatively short length scales. This duality is partly due

to the short-wave destabilization produced by conden-

sation heating. Short-wavelength cyclones with strong

condensation heating contain closed PV contours at finite

amplitude due to condensation heating. These systems

exhibit both wavelike and vortexlike characteristics. The

distinction between convective systems and baroclinic

cyclones becomes blurred. Untangling this duality is

central to understanding the dynamical identity of phe-

nomena such as subtropical cyclones in which conden-

sation processes are prominent.

The present paper attempts to clarify the dynamical

characteristics of subtropical cyclones through the use

of an idealized baroclinic channel model with parame-

terized effects of condensation heating. The model is

the Advanced Research Weather Research and Fore-

casting model (ARW-WRF, hereafter ARW), configured

as described in section 2. A baroclinic jet whose strength

is systematically varied is introduced. Horizontal shear, of

varying strengths in different simulations, is introduced in

an attempt to induce anticyclonic wave breaking. Abun-

dant moisture is present because the entire domain is over

ocean whose surface temperature is controlled by the

initial north–south temperature variation. The aim of the

study is to see what cyclone structures develop equator-

ward of the primary cyclone that forms within the mid-

latitude jet and to understand the basic mechanism of

formation of these cyclones.

The paper defines a set of diagnostic methods that

help to explain how the origin of subtropical cyclones

departs from the formation of midlatitude cyclones (sec-

tion 2). The basic effect of condensation in contrasting

pairs of simulations is evaluated in section 3. Section 4

elucidates the development paths of several cyclones

and quantifies the formation of one subtropical cyclone

in particular. Section 5 rounds out the parameter space

of varying meridional shear, midlatitude jet strength,

and condensation heating. The dichotomous behavior of

these simulations regarding whether extratropical or

subtropical systems dominate the long-term solution is

summarized in section 6.

2. Methods

The ARW is a nonhydrostatic, primitive equation

model described in Skamarock et al. (2005). The present

application is in an idealized framework that is similar to

the generic baroclinic wave test case available in WRF.

However, the present model configurations are relatively

more complex.

The model atmosphere is divided into a troposphere

and stratosphere following Plougonven and Snyder (2007),

who built on work by Rotunno et al. (1994) and Heckley

and Hoskins (1982). The PV distribution in the initially

purely zonal flow is specified by the height of the tro-

popause, which is a hyperbolic tangent profile in the y

direction, centered at the latitude of the westerly jet yJ.

The PV in the troposphere is not uniform because of the

addition of b 5 df/dy, where f is the Coriolis parameter.

Here, b is fixed at 10211 m21 s21. The PV is inverted for

the wind and potential temperature fields, which are

assumed to be in geostrophic balance. The boundary

conditions on the zonal velocity are homogeneous ex-

cept for the lower boundary upon which a meridionally

2872 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 67

varying zonal mean wind is prescribed. This constitutes

the inclusion of ‘‘barotropic’’ shear in the model, al-

though the meridional shear in the final state will not

be strictly barotropic. Thus, we refer to this as hori-

zontal shear or ‘‘bottom shear,’’ although the shear will

have units of velocity and represent the amplitude of

the sinusoidally varying zonal surface wind. The sur-

face zonal wind is specified poleward of y0 as uS 5

�S sin[2p(y� y0)/(D� y

0)], where D is the full merid-

ional extent of the model domain (10 000 km) and S

is the amplitude of the shear. The upper-tropospheric

jet is centered at (D 1 y0)/2 such that the anticyclonic

shear is maximized at the location of the jet. The ini-

tial surface wind is set to zero south of y0, where

y0 5 1000 km. Examples of the initial basic-state zonal

flow appear in Fig. 1. The parameters varied are the

amplitude of the tropopause transition, which translates

nearly linearly into a maximum jet speed U, and S. The

nomenclature for simulations is Smm_Unn, where mm

refers to the value of S and nn is the strength of the

initial U (Table 1). Hence, S15_U30 is a simulation with

a bottom shear of amplitude 15 m s21 and 30 m s21

westerly jet at the tropopause.1 We also use a suffix D to

denote a ‘‘fake-dry’’ integration. In these fake-dry sim-

ulations, surface heat, moisture, and momentum fluxes

remain on, but there is no condensation heating or

cooling. In some simulations, condensation heating is

removed after a specific time. These simulations are

referred to by appending this time in hours after D.

The model domain is periodic in the x direction with

a domain length of 4000 km. The horizontal grid spacing

for the simulations presented is 50 km. There are 60

vertical levels, stretched between a vertical spacing of

about 100 m near the surface to greater than 500 m at

the model top at 27 km. The model is initialized with

a fake-dry, adiabatic, nearly inviscid normal mode ob-

tained by a breeding method (Plougonven and Snyder

2007). Surface fluxes are turned off during the integra-

tion of the normal mode. The initial maximum ampli-

tude of the mode, which occurs at the tropopause, is set

to 2 K. Some simulations will be integrated with in-

finitesimal initial amplitude as described in section 4.

The model is integrated forward with physical pa-

rameterizations that include the Kain–Fritsch cumulus

parameterization (Kain 2004), the Yonsei University

boundary layer scheme (Noh et al. 2003), and the WRF

single-moment microphysics scheme (WSM5), which pre-

dicts rain, snow, cloud water, and cloud ice but only

distinguishes liquid and ice phases based on temperature.

Horizontal mixing is treated with a two-dimensional de-

formation-dependent mixing coefficient as well as a sixth-

order hyperdiffusion with a constant coefficient.

The model domain is entirely over ocean, with the sea

surface temperature (SST) prescribed to be 0.5 K greater

than the initial atmospheric temperature at the lowest

model level (about 40 m MSL). The SST will therefore

vary among the different experiments according to the

baroclinicity. To maintain some consistency between

simulations we adjust the basic state so that the maximum

SST in the domain is close to 308C. The tropospheric hu-

midity is uniformly 50% so that the maximum water vapor

mixing ratio in each simulation is initially about the same.

In the warmer regions, the initial moist thermodynamic

FIG. 1. Zonally averaged zonal wind [black contours; contour

interval (CI) 5 5 m s21), u (red, CI 5 5 K) and PV (grayscale;

PVU) for (a) S15_U30, (b) S15_U40, and (c) S10_U30 at t 5 0 h.

Thick red line is 330-K isentrope; thick dashed line is zero wind

line. Flow into the page is shown with thin solid lines.

1 After interpolations and an initialization procedure to remove

spurious oscillations (Plougonven and Snyder 2007), the actual jet

maximum speed may deviate by up to 1 m s21 from the number

indicated in the name of the simulation.


stability is nearly the same in all simulations as a result.

Substantial conditional instability, represented by con-

vective available potential energy (CAPE), exists in the

initial state over the warmest water in the domain and is

generally released before the mode on the jet grows to

appreciable amplitude. Significant convective inhibition

(CIN) also exists at the start of each simulation but it is

reduced because of fluxes from the ocean surface. The

strength of the initial surface winds is directly pro-

portional to S. Deep convection breaks out sooner for

stronger bottom shear and does so in easterly flow.

A variety of cyclones develop in the various simula-

tions performed and these are analyzed in a cyclone-

following framework. We first utilize a cyclone tracking

algorithm (Davis et al. 2008). Vorticity at 900 hPa at all

points is first replaced by the average over an 11 3 11

gridpoint box (500 km 3 500 km) centered on each

point. Maxima in area-averaged vorticity are tracked

using a 6-h time interval, and parameters are computed in

a system-following frame of reference. Vorticity maxima

must attain values of 2 3 1025 s21 to be included.

The tracking algorithm uses the linear extrapolation

of cyclone motion over the previous 12 h as a guess for

the position 6 h hence. If a vorticity maximum exceeding

the intensity constraint is found within 400 km of this

position, it is assigned as a continuation of the previous

vorticity maximum. If no vorticity maximum is found,

the track ends. If a vorticity maximum is found with no

preceding position, it is tracked as a new feature.

Because condensation heating is significant for the

oceanic cyclones in the simulations, it is useful to know

how the relative importance of condensation heating and

baroclinic processes changes from storm to storm, and

during the life cycle of a given cyclone. Two existing

measures of these contributions avail themselves. First is

the energy conversion diagnostic (Lorenz 1955; Parker

and Thorpe 1995; Moore and Montgomery 2005) wherein

the rates of generation of eddy available potential energy

(APE) by diabatic processes and conversion of mean

available potential energy are compared. Another

commonly used diagnostic is the phase space diagram

(Hart 2003), in which the instantaneous structure of the

cyclone is described using parameters that measure the

lower-tropospheric geostrophic vertical wind shear and

the vertical structure of the layer thickness anomalies

above the cyclone center.

The energy conversion diagnostic provides time

tendency information and quantifies the diabatic heat-

ing contribution to the generation of eddy APE through

the correlation of heating and temperature anomalies.

The adiabatic contribution is proportional to the me-

ridional heat flux, tempered by the adiabatic cooling

term that generally opposes this flux. In essence, this

term measures the instantaneous meridional movement

of isentropes by eddies. In contrast, the cyclone phase

space diagram describes the structure of the cyclone

itself but only indirectly indicates the processes in-

volved.

In the present study we utilize a different metric that

is based on Ertel PV, generalized to include potential

temperature anomalies on the lower boundary, in prac-

tice at the top of the planetary boundary layer (around

900 hPa). Bretherton (1966) was the first to recognize

formally that an inhomogeneous surface potential tem-

perature distribution was equivalent to a homogeneous

distribution plus a sheet of infinite PV an infinitesimal

distance above the ground. This uses the fact that a dis-

continuous jump in potential temperature is synonymous

with a delta function in PV. The resulting PV has a finite

vertical integral and thus may be compared to a verti-

cally integrated PV anomaly that exists elsewhere in the

flow. The advantage of casting lower-boundary temper-

ature anomalies in terms of PV is that baroclinic and

condensation heating influences on cyclone structure can

be compared directly. The near-surface baroclinicity is

represented as a PV anomaly defined as follows:

PV1 5 ghG/Dpref

, (1)

where

TABLE 1. Simulations analyzed in the present study. Units for U and S are meters per second. Simulation names appear in the ap-

propriate cells. A dash indicates that no simulation was performed for that combination of parameters. Suffix D120 refers to simulation

that is run in fake-dry configuration after 120 h; suffix C refers to simulations with temperature reduced by 5 K; suffix NOMODE refers to

simulation with initial mode amplitude set to 0.001 K; suffix GD refers to the use of the Grell–Devenyi cumulus scheme; and suffix DX25

refers to simulation S15_U40_NOMODE run with a grid spacing of 25 km.

U 5 25 U 5 30 U 5 35 U 5 40 U 5 50

S 5 5 — S05_U30 — — —

S 5 10 — S10_U30 — S10_U40 —

S 5 15 S15_U25 S15_U30, S15_U30_D,

S15_U30_D120, S15_U30_C

S15_U35 S15_U40, S15_U40_D, S15_U40_D120,

S15_U40_NOMODE, S15_U40_C,

S15_U40_GD, S15_U40_DX25

S15_U50


G 5 (G2x 1 G2

y)1/2,

Gx

51

L

ðL/2

�L/2

u9 dy

��x5L/2

� 1

L

ðL/2

�L/2

u9 dy

��x5�L/2

,

Gy

51

L

ðL/2

�L/2

u9 dx

��y5L/2

� 1

L

ðL/2

�L/2

u9 dx

��y5�L/2

,

h is the absolute vorticity, and u9 is the deviation of po-

tential temperature from the zonal mean. The coordinate

(0, 0) is the cyclone center. The potential temperature

variations (Gx, Gy) are averaged at two pressure levels,

900 and 850 hPa, prior to computing G. Furthermore,

L 5 1000 km and the vertical scale Dpref is chosen to be

400 hPa to match the range of vertical integration of

interior PV (see below).

The interior PV, representing primarily the conden-

sation heating influence, is defined by the volume in-

tegral of perturbation PV:

PV2 5

ðL/2

�L/2

dx

ðL/2

�L/2

dy

ðp2

p1

q9 dp

L2Dpref

, (2)

where q9 is the deviation of PV from the zonal mean,

p1 5 500 hPa and p2 5 900 hPa, and Dpref 5 p2 2 p1.

Averaging between these pressure levels generally

avoids contributions to the PV from tropopause un-

dulations. In general, we examine the ratio PV1/PV2, in

which Dpref does not appear explicitly.

The goal in devising the PV metric is to have a simple

measure of the contributions of lower-tropospheric baro-

clinic processes and condensation heating to the behavior

of cyclones. Although the parameters are evaluated in-

stantaneously, they embody the accumulated effects of

baroclinic and condensation processes. Furthermore, time

dependence of these parameters gives insight into the

changing character of individual cyclones. This is quali-

tatively similar to some of the information obtained from

cyclone phase space diagrams. It should be noted that

these PV metrics cannot generally provide dynamical

information about cause and effect. For instance, it is

entirely possible that weak baroclinicity can still cata-

lyze intense condensation heating.

To understand how the baroclinic dynamics are linked

to thermodynamic destabilization and the organization

of deep convection, we use the quasigeostrophic omega

equation (Bluestein 1992):

s=2v 1 f 20

›2v

›p25�2$ � Q, (3)

where s[5(kp/p)(›Q/›p)] is the quasigeostrophic sta-

bility parameter, k 5 R/Cp, p is the Exner function,

Qf52(R/p)[(›vg/›x) � $pT, (›vg/›y) � $pT]g is the

Q vector computed on pressure surfaces, subscript g de-

notes geostrophic, and the constant f0 is the average value

of the Coriolis parameter in the domain (51024 s21).

The variation of the Coriolis parameter has also been

neglected on the right-hand side of (3). The stability pa-

rameter at each level represents the horizontal average

across the domain. Periodic boundary conditions in the

zonal direction and homogeneous upper and lower

boundary conditions on v are applied, with the top at

100 hPa. A relaxation solver is used, obtained from the

Read/Interpolate/Plot program of the WRF system.

3. Large-scale effects of condensation

In Fig. 2, snapshots during the evolution of four dif-

ferent simulations are presented. The simulations with

a weaker jet, S15_U30 and S15_U30_D (Figs. 2a,c),

produce notably different solutions both from each

other and from the solutions with the 40 m s21 jet (Figs.

2b,d). The solution in S15_U30_D somewhat resembles

the solution in S15_U40_D but grows more slowly and

hence is less amplified at a given time. The surface fronts

are comparatively weak and do not penetrate into lower

latitudes at this point.

Simulation S15_U30 produces a strong cyclone (C1)

that forms in the easterlies around y 5 3000 km and

rapidly intensifies and turns northward (Fig. 2a). The

evolution of C1 is shown in Fig. 3. This cyclone begins at

lower latitudes as an inverted trough in easterly flow by

day 5 (Fig. 3a). It rapidly intensifies with strong diabatic

heating and minimal near-surface baroclinicity (not

shown) to become a deep cyclone by day 8 (Figs. 3b,c).

The strong diabatic heating produces a deep column of

cyclonic PV as indicated by PV greater than 2 PV units

(PVU; 1 PVU 5 1026 m2 K21 kg21 s21) even visible on

the 330-K surface (8–9-km altitude) within the cyclone

circulation starting at day 6.5. Cyclonic PV extending to

this altitude has been observed in hurricanes (Shapiro

and Franklin 1995). The development of C1 appears

independent of development on the midlatitude jet.

Cyclone C1 also dominates the PV changes in the up-

per troposphere where the appearance of anticyclonically

curved outflow (not shown) provides a strong upper-

tropospheric ridge while at the same time contributing

to the southward extrusion of a narrowing PV filament

(Fig. 2a). This filament is associated with a weak surface

disturbance and area of convection in easterly flow. The

cyclone that grows from this disturbance (C2) will be

discussed below. Of note is that, despite the anticyclonic

shear, the effect of condensation heating has resulted in

a dominance of cyclonic circulation in the lower tropo-

sphere, as well as even stronger anticyclonic PV signatures


in the upper troposphere than are produced in the fake-

dry simulation. This is consistent with the expected re-

arrangement of PV from condensation heating, wherein

the PV in the upper troposphere decreases and PV in the

lower troposphere increases.

Simulations S15_U40 and S15_U40_D (bottom shear

amplitude 15 m s21, westerly jet 40 m s21, ‘‘D’’ for

fake-dry; see section 2) are generally similar to each

other at 264 h (Figs. 2b,d). The bottom shear has in-

duced anticyclonic wave breaking seen in the PV and led

to the dominance of the anticyclones over cyclones. The

primary baroclinic cyclone that represents the evolution

of the normal mode has progressed well into the non-

linear regime and has migrated to the far northern part

FIG. 2. PV on 330-K isentropic surface (grayscale; PVU), 6-h precipitation (color; mm) and SLP (magenta;

CI 5 4 hPa) for (a) S15_U30 at 240 h, (b) S15_U40 at 264 h, (c) S15_U30_D at 240 h, and (d) S15_U40_D at 264 h.

Domain has been repeated in the x direction to more clearly show structures. Thin purple zonal line between

y 5 4000 km and y 5 5000 km denotes the 268C SST isotherm. The string of blue diamonds in (a) is the track of

C1 with positions shown every 6 h.


of the domain near y 5 9000 km (Figs. 2b,d). Two sec-

ondary cyclones have developed in both the dry and

moist simulations on the eastern and southeastern flank

of the cyclonic PV feature. These are located along y 5

7500 km and y 5 5000 km. In the moist simulation

a separate cyclone (C3) has developed still farther south

near y 5 3000 km. This cyclone has a region of heavy

rainfall on its northern flank. Boundary layer tempera-

ture (not shown) indicates that a warm frontal structure

coexists with the heavy rainfall and a weak cold front

extends south of the cyclone with attendant light con-

vective precipitation.

A graphical summary of the simulations shown in

Fig. 2 is obtained by constructing a Hovmoller diagram

of the maximum PV at each latitude on the 330-K sur-

face, qmax(y, t). In addition, it is useful to compute the

fraction of PV along a given latitude above or below a

fixed value. Condensation heating is expected to change

such a fraction irreversibly. We compute the fraction of

PV less than 1 PVU as a function of y, termed qfrac(y, t).

Hence a value of 0.75 means that PV was less than 1

PVU over 75% of the zonal extent of the domain at that

latitude.

The Hovmoller diagrams of qfrac(y, t) and qmax(y, t)

support the statement that condensation heating quali-

tatively changes the solution in S15_U30 (Figs. 4a,b).

Initially both quantities have a simple meridional vari-

ation, with qfrac(y, t) essentially constant north and south

of a narrow transition zone and qmax(y, t) representing

the initial variation of PV on the 330-K surface (see

Fig. 1a). The result of condensation heating in S15_U30

is clearly a dramatic increase in the meridional rearrange-

ment of PV relative to what happens in the dry simula-

tion. Not only is there enhanced anticyclone development

at high latitudes, but high PV is transported to low lati-

tudes where it then influences further cyclone develop-

ment.

The tracks of cyclones moving poleward from lower

latitudes are seen as ribbons of enhanced maximum PV

values in the simulations with condensation heating. In

FIG. 3. SLP (CI 5 4 hPa), 2-PVU contour (heavy contour) on the 330-K isentropic surface, and relative vorticity at 900 hPa from

simulation S15_U30 at (a) 120, (b) 156, and (c) 192 h.


FIG. 4. Hovmoller diagrams of qmax (color, PVU) and qfrac (0.25 and 0.75 contours) as a function

of y and t for (a) S15_U30, (b) S15_U40, (c) S15_U30_D, and (d) S15_U40_D.


S15_U30 (Fig. 4a), the effect of the cyclone is to rapidly

build a ridge through diabatic processes. This is seen

primarily in the qfrac(y, t) parameter. Ridge devel-

opment in S15_U30 follows the poleward movement of

cyclone C1 (Fig. 4a) while another cyclone, C2, forms at

relatively low latitudes and migrates poleward. No low-

latitude cyclones form in the dry simulation.

As seen in Fig. 2, the differences between dry and

moist simulations with a stronger jet (Figs. 4b,d) are not

as pronounced as with the weaker jet (Figs. 4a,c), al-

though the condensation effects are distinctly evident in

the rapid appearance of lower PV values at high lati-

tudes around 180 h. In S15_U40, the rapid ridge de-

velopment occurs prior to the formation of cyclone C3

(Fig. 4b) at low latitudes. This ridge development is part

of the development of the primary extratropical baro-

clinic wave. The low-latitude cyclone dissipates before

moving into the midlatitudes, in contrast to the low-

latitude cyclone developments in S15_U30.

4. Subtropical cyclones

In this section, we examine the dynamics of the low-

latitude cyclones that form in the moist simulations. The

primary tools are the set of cyclone-following diagnostics

outlined in section 2. Our definition of a subtropical cy-

clone will be one in which the initial development features

negligible baroclinicity and significant lower-to-middle-

tropospheric PV (assumed to originate from diabatic

heating) such that the ratio PV1/PV2 is nearly zero. Fur-

thermore, to distinguish subtropical and tropical cyclones,

we insist on deep and relatively strong vertical wind shear

oriented generally from a westerly direction during the

development process. Here ‘‘strong’’ means at least 10–

15 m s21 of shear over the troposphere between 900 and

300 hPa. DeMaria et al. (2001) noted that tropical cy-

clone formation was exceedingly rare when the zonal

component of the wind shear between 850 and 200 hPa

was westerly and exceeded 12.5 m s21.

The first cyclone examined is C1 from simulation

S15_U30. Time series of PV1 and PV2 parameters in-

dicate that this cyclone is almost entirely a manifesta-

tion of diabatic heating early in its evolution (Fig. 5a).

Around the time that the cyclone achieves its maximum

intensity the baroclinicity begins increasing notably. But

from an equivalent PV perspective, the contribution

from baroclinicity always remains far below the interior

PV contribution. The vertical wind shear, averaged

within a cyclone-centered box 1000 km on a side and

expressed as the magnitude of the velocity difference

between 900 and 300 hPa, was 16.6 m s21 averaged over

the cyclone development stage (90–192 h). The vertical

shear at the beginning of the track is westerly at about

13 m s21, so it is clear that C1 experienced moderate

vertical wind shear throughout its development. We

argue that C1, because of its dependence on condensa-

tion heating, its near absence of lower-tropospheric

baroclinicity, and its formation in moderate, deep, west-

erly shear, should be denoted a subtropical cyclone.

Surface cyclone C2 forms on the east side of an elon-

gated upper-tropospheric PV filament that forms in re-

sponse to the outflow from C1 (Figs. 2a and 4a). The PV

time series for this cyclone indicates that it, too, has almost

no baroclinic contribution initially and is therefore similar

to C1 (Fig. 5b). The vertical shear over C2 during its de-

velopment is southwesterly, averaging around 10 m s21.

Thus, C2 is also designated as a subtropical cyclone.

The PV parameter time series for the primary cyclone

(near y 5 9000 km in Fig. 2b) in the simulation with the

stronger jet (U 5 40 m s21) is consistent with expecta-

tions of PV components of a growing baroclinic wave.

The time series of the primary cyclone in the fake-dry

simulation (S15_U40_D) is shown in Fig. 6a. This may

FIG. 5. Time series of (a) vorticity (thin black), PV1 (dashed

black), PV2 (thin gray), and PV1/PV2 (thick gray) for cyclone C1

from simulation S15_U30, and (b) vorticity and ratio PV1/PV2

for cyclone C2 from simulation S15_U30. Vorticity is in 1024 s21

and PV is in PVU.


be compared with the time series from the moist simu-

lation in Fig. 6b. In both cases the baroclinic contribu-

tion dominates the interior PV contribution early on.

There appears to be a nontrivial contribution from the

interior PV even in the dry simulation. Recall that this

simulation was run with a boundary layer parameteri-

zation and surface fluxes. We surmise that the positive

PV anomaly is produced at the top of the boundary layer

as a result of the turbulent mixing below, which re-

distributes PV in the vertical. The appearance of cy-

clonic PV anomalies from mixing was described in detail

by Stoelinga (1996). In the moist case, the interior PV

contribution (PV2) becomes notably larger and the

maximum intensity of the cyclone nearly doubles rela-

tive to the dry case. We may infer that condensation

effects rapidly increase in their importance around the

beginning of day 7 (144 h) when the cyclone intensity

abruptly increases and departs from the time series for

the dry cyclone.

Cyclone C3 (see Fig. 4b), which later develops in

S15_U40, is highlighted in Fig. 6c. The time series shows

that the initial cyclone has essentially zero baroclinic

contribution, at least as judged by lower-tropospheric

temperature gradients. The primarily influence is the

cyclonic PV in the lower troposphere that we infer arises

from condensation heating. Near the time of maximum

intensity of this cyclone, baroclinic influences become

more prominent. Although the details differ, this cy-

clone is similar in its PV partitions to cyclones C1 and C2

from S15_U30. Note also that the vertical shear between

900 and 300 hPa averaged about 14 m s21 from a west-

erly direction during the development phase, again sim-

ilar to C1. Given its similarity with C1 and C2, we term C3

a subtropical cyclone as well.

Cyclone C3 emerges following the development of

a Rossby wave on the tropopause in conjunction with

the formation of a subtropical jet stream, but also ap-

parently with some influence from the southward pen-

etration of the primary trough from the midlatitude

baroclinic wave. Recall that in simulation S15_U30 the

subtropical cyclone developed more rapidly than the

extratropical cyclone and hence dominated the solution.

In S15_U40, subtropical and extratropical developments

overlap in time. Shown in Fig. 7 are maps of potential

temperature on the dynamic tropopause uTR, here de-

fined as a surface of constant PV (52 PVU). Fields are

interpolated vertically to this surface from the two

model levels that bracket the PV 5 2-PVU surface,

based on a downward search starting at the top of the

model. The view of Rossby waves from the dynamic

tropopause perspective appears in Morgan and Nielsen-

Gammon (1998) and is similar to the view of undulating

PV contours on an isentropic surface, except here it is

represented as undulations of potential temperature con-

tours on a PV surface.

At 120 h the undulations of uTR contours are associ-

ated with the primary baroclinic wave development over

the northern portion of the domain shown (Fig. 7a; note

that the model domain extends 3000 km farther north).

Farther south, scattered precipitation, nearly all pa-

rameterized, occurs from y 5 2000 km to y 5 2500 km.

A well-defined gradient of potential temperature exists

FIG. 6. Time series of maximum area-averaged relative vorticity

(black) and ratio PV1/PV2 (gray) for (a) the primary baroclinic

cyclone in S15_U40_DRY, (b) the primary baroclinic cyclone in

S15_U40, and (c) the secondary (subtropical) cyclone in S15_U40.

Vorticity is in 1024 s21.


FIG. 7. Maps of uTR and winds on PV 5 2-PVU surface, SLP (CI 5 4 hPa) and 6-h accumulated precipitation from

simulation S15_U40 at (a) 120, (b) 168, (c) 216, and (d) 264 h. The domain shown spans y 5 1000 km to y 5 7000 km.

Thin purple zonal line near y 5 4200 km denotes 268C SST isotherm.


immediately poleward of this weak convection. By 168 h

the low-latitude uTR contours exhibit waviness, as do the

tropopause winds (Fig. 7b). The convection now appears

slightly more localized to the east of the trough. This

wave amplifies and appears to merge with a southward

extrusion of low-uTR air from the primary baroclinic

wave. This forms a relatively robust upper-tropospheric

wave by 216 h as a weak cyclone forms at y 5 2500 km

with well-organized deep convection (Fig. 7c). The cy-

clone then amplifies and intense convection rapidly

builds an anticyclone on the tropopause with attendant

strong westerlies on the poleward flank of the tropo-

pause anticyclone near y 5 4500 km (Fig. 7d).

On the equatorward side of the tropopause anticy-

clone there is an easterly jet, but there is little hint of

undulation of the associated potential temperature gra-

dient until the subtropical cyclone is well developed (Figs.

7c,d). The lack of development on the easterly jet is

probably due to the near absence of surface winds that

might destabilize the atmosphere with respect to moist

convection.

Viewed from an eddy and mean-flow perspective on

the tropopause, it is clear that the early convection in the

moist simulation fundamentally changes the zonal mean

of u on the tropopause by forming a local maximum over

the southern part of the domain (Figs. 8a,c). To assist with

interpretation we have integrated a separate simulation

beginning with the moist-simulation state at 120 h but

thereafter allowing no condensation heating or cooling

(simulation S15_U40_D120). This simulation maintains

a sharpened gradient of uTR near y 5 2500 km as well

as the minimum of uTR further south. This sharpened

gradient of uTR corresponds to a secondary zonal wind

maximum that we interpret as a subtropical jet. In

S15_U40_D120 this jet remains anchored at y 5 2500 km,

but in the moist simulation the jet moves poleward with

time as the subtropical storm amplifies (Fig. 8a).

Furthermore, it appears that the midlatitude wave in-

fluences the subtropical disturbance beginning around

day 8 based on the eddy fluxes of uTR (Fig. 8b). Here the

analogy of eddy PV flux is the eddy flux of potential

temperature on the tropopause. Positive fluxes indicate

wave amplification and changes in the zonal mean. To

assess the influence of the extratropical baroclinic wave

on the low-latitude cyclone formation, we integrated an

additional simulation (S15_U40_NOMODE) in which

the initial normal mode amplitude was set to 0.001 K.

Development of a subtropical cyclone proceeded some-

what like that shown in Fig. 7 but with no discernable

influence from midlatitudes (Fig. 8h). In fact, the re-

sulting cyclone became a powerful cyclone in the ex-

tratropics, similar to the evolution of the subtropical

cyclone in S15_U30 (Fig. 2a). More description of

simulation S15_U40_NOMODE can be found at the end

of section 5.

In each simulation with condensation heating during

the first five days, the redistribution of PV due to the

heating produces a zonally averaged state with a reversal

of the meridional PV gradient on isentropic surfaces,

and a reversal of the meridional gradient of potential

temperature on the tropopause. The former can clearly

be seen in Fig. 9b. In comparison, Fig. 9a shows no re-

versal of the PV gradient. Because of this reversal of PV

or uTR gradients, we infer that the necessary condition

for baroclinic or mixed barotropic and baroclinic in-

stability is satisfied. If the heating is shut off after day 5,

there eventually emerges a growing mode structure on

the subtropical jet around day 10 (Fig. 8d), but wave

growth is slow in comparison with growth on the mid-

latitude jet without diabatic heating (e.g., Fig. 8f).

Two points may be inferred from the preceding anal-

ysis. First, the midlatitude baroclinic wave in S15_U40 is

mainly a hindrance to the full development of the sub-

tropical cyclone. We surmise that the negative influence

is both through increasing horizontal deformation and

vertical wind shear associated with the southward-moving

polar front. However, because the initial development of

the subtropical cyclone does not depend appreciably on

the midlatitude baroclinic wave, the phase relation be-

tween the two systems is effectively random. This means

that the inhibiting configuration of the midlatitude system

in the present simulation may depend on the detailed

phase relation of midlatitude and subtropical systems.

Such is the case in extratropical transition (Ritchie and

Elsberry 2007).

The second point is that the development of the sub-

tropical cyclone results from a moist instability of the

subtropical jet. There is no evidence of such a distur-

bance, of any amplitude, in the adiabatic simulation.

Even in a basic state with a subtropical jet and reversal

of the PV gradient, the disturbance grows slowly without

condensation heating. Once heating is allowed the dis-

turbance grows rapidly. This sharply contrasts with the

midlatitude development wherein the inclusion of dia-

batic heating provides a modest enhancement of growth.

Part of this difference may be anticipated because of the

enhanced water vapor mixing ratio available to the sub-

tropical disturbance owing to its development over warm

water. This issue will be addressed in section 5.

A remaining question is how wave activity on the tro-

popause affects the tropospheric thermodynamic state to

promote deep convection. To address this we solve the

quasigeostrophic omega equation as described in section

2, using the model-derived geopotential field from

S15_U40_D120 at 168 and 216 h (Fig. 10). Vertical cross

sections show that the lifting is weak but persistent and


located on the downshear (east) side of the tropopause-

based trough. The relative humidity responds by increas-

ing to nearly 80% over a deep layer. Lifting of 0.5 cm s21

produces a vertical displacement of about 1 km in 2 days,

which can easily increase the humidity by 20%–30%.

In Fig. 10 we also note that there is essentially no merid-

ional velocity signature of the wave in the middle and

lower troposphere. Rather, the structure resembles an

evanescent wave on the tropopause. In this circumstance,

the lifting is almost entirely due to the tropopause

FIG. 8. Hovmoller (y vs t) of (left) zonal mean uTR and (right) eddy flux of uTR on the dynamic tropopause, for (a),(b) simulation

S15_U40, (c),(d) S15_U40_D120, (e),(f) S15_U40_D, and (g),(h) S15_U40_NOMODE. The cross in the bottom panels is a reference

marker that marks the beginning of wave growth on the subtropical jet in S15_U40_D120.


perturbation. Juckes and Smith (2000) investigated the

convective destabilization from lifting induced by tro-

popause-based troughs in tropical atmospheres and

concluded that even modest tropopause-based troughs

can dramatically reduce CIN and increase CAPE. The

present results appear consistent with that idea.

In the moist simulation, however, once convection

organizes there is generation of surface cyclonic vortic-

ity and eventually a deep cyclone results (Fig. 11). There

is a signature of a PV anomaly produced by condensa-

tion in the middle troposphere. Note that the adiabatic

quasigeostrophic omega is also much larger during cy-

clogenesis. The structure depicted in Fig. 11 appears

similar to that of a baroclinic cyclone, but there is almost

zero baroclinicity in the lower troposphere during the

early stages of development. Baroclinicity eventually in-

creases as the cyclone develops, especially after the cy-

clone moves to higher latitudes.

5. Other simulations

In this section we examine the overall sensitivity of

results to varying the basic-state vertical and horizontal

shear as well as sensitivity to use of different parame-

terizations. In Fig. 12 are shown results from experiments

with varying bottom shear and westerly jet strength at

either 240 or 264 h depending on the simulation. Across

the top row, the bottom shear is a constant S 5 15 m s21

whereas the jet strength U is 25, 35, and 50 m s21 in

panels a, b, and c, respectively. Much like the first sim-

ulation shown in Fig. 1, S15_U25 produces a strong cy-

clone at low latitudes that becomes a powerful

extratropical cyclone (Fig. 12a). This is perhaps not sur-

prising because we already argued that baroclinic waves

on a westerly jet of 30 m s21 did not grow fast enough to

influence the low-latitude development. Disturbances on

the weaker jet will grow even more slowly. In fact,

a simulation in which the midlatitude tropopause jet was

FIG. 9. Zonally averaged cross sections of zonal wind (black;

CI 5 5 m s21), PV (grayscale; PVU) and pressure (red; CI 5

100 hPa). The vertical coordinate is u. Times shown are (a) t 5 0 h

and (b) t 5 180 h from simulation S15_U40. The zero wind line is

dashed. Flow into the page is shown with thin solid lines.

FIG. 10. Quasigeostrophic v [0.1 Pa s21 (i.e., mb s21); blue de-

notes upward motion], PV (grayscale; PVU), meridional wind

(zero line omitted; heavy lines for positive values; CI 5 2 m s21),

and relative humidity (CI 5 20%, beginning at 60%). Cross sec-

tions are oriented west–east, centered at y 5 3000 km and averaged

250 km north and south of the centerline. Fields are shown at (a)

168 and (b) 216 h, both from simulation S15_U40_D120.


completely removed produced a subtropical cyclone de-

velopment qualitatively similar to that shown in Fig. 12a

(not shown). The cyclone shown in Fig. 12a is a sub-

tropical cyclone by our definition.

In S15_U35 (Fig. 12b), the result parallels S15_U40

in that a low-latitude cyclone emerges with a similar

structure. Simulation S15_U35 also presents a compe-

tition between the subtropical cyclone development

and the southward development of the cyclonic PV

trough from midlatitudes. Outflow from subtropical

convection intensifies the westerlies near the central

latitude of the domain. This westerly subtropical jet

appears to impede the southward progression of the

extratropical trough by literally stripping PV from the

trough through strong horizontal shear. The associated

‘‘barrier’’ effect (Dritschel and McIntyre 2008, and ref-

erences therein) is well known to occur on the edge of

the polar jet. However, careful comparison of Fig. 12b

and Fig. 7d reveals that the zonal phase relationship

between the subtropical cyclone and baroclinic wave is

different from that in S15_U40. While the subtropical

cyclone in S15_U40 decays after 264 h, the subtropical

cyclone in S15_U35 becomes positioned to the east of

the midlatitude trough and enjoys a period of renewed

development at higher latitudes (not shown).

In the simulation with the strongest jet, S15_U50 (Fig.

12c), no subtropical cyclone develops. A frontal second-

ary cyclone forms primarily through baroclinic processes.

The influence of the primary baroclinic wave, manifested

as a southward extrusion of high-PV air, is strongest in

S15_U50. Note that the basic state for this simulation, and

the resulting evolution, are broadly similar to the LC1

results from Thorncroft et al. (1993).

In the second row of Fig. 12 are shown results from two

simulations where S 5 10 m s21. The simulation with U 5

30 m s21 forms a closed anticyclone on the tropopause

wherein the low-PV air that results from the deep con-

vection ‘‘pools’’ within the closed circulation (Fig. 12d).

A cyclone with subtropical characteristics eventually

emerges in this simulation, but not until day 12. When

the westerly jet increases to 40 m s21 (Fig. 12e), essen-

tially no subtropical cyclone activity occurs. Secondary

cyclone formation occurs in response to the southward-

moving trough. Based on the temperature gradients and

the gradient of sea level pressure poleward of the cy-

clone center, the secondary cyclone in S10_U40 is con-

siderably weaker than the one in S15_U50 but the

overall behavior is qualitatively similar.

The result from the lone simulation performed with S 5

5 m s21 is depicted in Fig. 12f, for which U 5 30 m s21.

This simulation represents a similar evolution to that in

S15_U50 and S10_U40, although with the weakest sec-

ondary cyclone of all. Thus, it appears that decreasing the

westerly jet strength and the bottom shear simultaneously

can result in a similar evolution qualitatively.

Time series of PV parameters representing the sec-

ondary cyclones in S10_U40 and S05_U30 clearly show

that both begin as baroclinic cyclones because PV1/PV2

is near unity or greater (Fig. 13). This distinguishes such

cyclones dynamically from subtropical cyclones despite

their formation at a relatively low latitude. During the

development of these cyclones the vertical wind shear

(900–300 hPa) is about 10–15 m s21 from the southwest

in S05_U30 and 25–29 m s21 from the south in S10_U40.

The latter is nearly twice as large as that found typically

for subtropical cyclones in simulations presented earlier.

In S05_U30, deep convection does not develop at low

latitudes and therefore the subtropical tropopause is

largely undisturbed from its initial configuration. With

the weak surface winds that accompany S 5 5 m s21, the

thermodynamic destabilization from moisture fluxes from

the ocean is relatively absent and deep convection does

not develop. As a consequence, there is little diabatically

induced PV change in the upper troposphere and the

subtropical jet stream remains weak.

All the simulations discussed so far used essentially

the same thermodynamic profile over the southern part

of the domain, namely, with relatively large CAPE of

roughly 3000 J kg21 for the most unstable, undilute

parcel. The large CAPE was partly a response to fluxes

of water vapor from the ocean. These fluxes also de-

stabilized the atmosphere by reducing CIN. It is clear

that deep convection was responsible for altering the

basic state to produce a subtropical jet on the dynamic

tropopause. A reasonable question is therefore how

sensitive this behavior is to the thermodynamic state. In

FIG. 11. As in Fig. 10, but for simulation S15_U40 at 216 h.


FIG. 12. Tropopause maps as in Fig. 7, but for (a) S15_U25 at 240 h, (b) S15_U35 at 264 h, (c) S15_U50 at

240 h, (d) S10_U30 at 264 h, (e) S10_U40 at 264 h, and (f) S05_U30 at 264h. The thin purple zonal line denotes

the 268C SST isotherm.


particular, if CAPE were significantly reduced, what would

happen?

The most straightforward way to reduce CAPE and

the effects of condensation heating in general is to reduce

the temperature. This is done by decreasing potential

temperature everywhere in the domain by 5 K at the

start of the simulation. For a uniform change in potential

temperature, the adiabatic normal mode is unaltered.

However, this change effectively decreases the tropo-

spheric temperature and SST by the same amount. In this

case the maximum SST in the domain is about 258C,

compared to 308C in all the forecasts discussed pre-

viously. This reduction in SST decreases the mixing ratio

during the simulation by about 20%. CAPE is reduced

by roughly 30% and CIN stays about the same.

The simulations with the reduction in temperature

will be denoted by a ‘‘C’’ (for ‘‘cooler’’) appended to the

name. Repeating the two moist simulations shown in

Fig. 2 but with lower temperature still results in a sub-

tropical cyclone forming in S15_U30_C, but not in

S15_U40_C (Figs. 14a,b). The simulation with the stron-

ger jet produced a robust secondary cyclone beneath the

cold trough that was moving equatorward. In another

experiment with the same basic state as in S15_U40_C,

but with negligible amplitude in the normal mode,

a subtropical cyclone formed but required almost 15 days

to do so. It is clear that the strength of convection and

total condensation heating are important aspects of cre-

ating the basic state upon which a subtropical cyclone

grows.

Because of the importance of deep moist convection in

the formation and intensification of subtropical cyclones

in the present model, it is important to examine the sen-

sitivity of results to the cumulus parameterization. Even

for a given cumulus scheme, a change in model resolution

can produce different results. To investigate the sensi-

tivity to resolution and parameterization choices, we fo-

cus on the base state with the 40 m s21 jet. To isolate

better the subtropical development from midlatitude

development, and therefore enhance the relative impor-

tance of diabatic to baroclinic processes, we choose the

initial condition with the initial amplitude of 0.001 K. The

reference simulation, S15_U40_NOMODE was already

discussed in section 4. The other two simulations pre-

sented here include one in which the horizontal grid

spacing was decreased to 25 km (S15_U40_DX25) and

one using the Grell–Devenyi cumulus scheme (Grell and

Devenyi 2002) with the standard 50-km grid spacing

(S15_U40_GD).

Figure 15 contains a summary of the essential differ-

ences between the three simulations. An important dif-

ference is the relatively larger values of tropopause

potential temperature due to stronger convection in the

perturbed simulations between days 3 and 6. This can be

seen as a large area of uTR . 360 K (Figs. 15b,c) in the

perturbed simulations, whereas this area hardly exists in

the reference simulation and is induced mainly by the

developing storm itself (Fig. 15a). The greater convec-

tion results in a greater stabilization of the subtropical

atmosphere and delays the subsequent development of

the subtropical cyclone by several days. Nevertheless,

simulation S15_U40_DX25 produces a strong subtropical

cyclone (Fig. 15e) similar to that produced in the refer-

ence simulation with a similar time scale of intensification

once it starts. The slightly poleward location of the storm

(Figs. 15b,e) relative to the cyclone in the reference

simulation reflects the broadened anticyclone near the

tropopause with westerlies displaced poleward.

In S15_U40_GD, the midlatitude baroclinic wave

grows faster (Fig. 15c) so that it tends to dominate the

development process by days 15–17 (Figs. 15c,f). The

faster growth is a result of the greater condensation

heating produced by the Grell–Devenyi scheme. For-

mation of a low-latitude cyclone occurs as in other

simulations, but it is not clearly isolated from the higher-

latitude cyclone. Despite the apparent influence of the

midlatitudes, the cyclone near y 5 3000 km forms in the

near absence of lower-tropospheric baroclinicity and

has a PV1/PV2 ratio nearly zero (not shown). Since it

FIG. 13. Time series of cyclone-following maximum vorticity

(black) and PV1/PV2 (gray, dimensionless) for secondary cyclones

from (a) S10_U40 (cf. Fig. 10e) and (b) S05_U30 (cf. Fig. 10f).


occurs in westerly shear, this is a subtropical cyclone by

our definition. The simulation with the Grell–Devenyi

scheme produces more small-scale vortices than the ref-

erence simulation, as does the higher-resolution simula-

tion with the Kain–Fritsch scheme, but these vortices

appear relatively incidental to the ultimate subtropical

development.

6. Conclusions

The present study has utilized idealized, moist primitive

equation simulations to define dynamically subtropical

cyclones and distinguish these cyclones from extratropical

(and tropical) cyclones. The model used was the ARW,

initialized with adiabatic normal modes in a baroclinic

channel of length 4000 km and width 10 000 km that was

entirely over an ocean with prescribed surface tempera-

ture. The primary parameters governing the behavior

of these simulations appear to be the strength of the

westerly jet and the strength of the barotropic shear and

surface winds over low latitudes. Barotropic shear and

surface winds are linked by the specification of the initial

zonal wind on the lower boundary. The former causes

anticyclonic wave breaking of the midlatitude Rossby

waves. The latter cause convective destabilization through

surface fluxes where surface easterlies coincide with the

highest sea surface temperatures.

The important parameters are S, the amplitude of the

sinusoidally varying ‘‘bottom shear,’’ and U, the initial

maximum zonal westerly wind. When the ratio U/2S is

significantly greater than unity, simulations are domi-

nated by the evolution of the midlatitude baroclinic

wave. A variety of cyclones forms within this wave. The

primary cyclone is part of the normal mode that ini-

tializes the simulation. As the wave becomes nonlinear,

additional surface cyclones form on the flank of the

large-amplitude cyclonic tropopause PV anomaly. These

cyclones tend to form successively farther south as the

cyclonic PV trough penetrates to lower latitudes. The

southward penetration increases for increasing U. This

scenario is represented by the schema in the left column

of Fig. 16.

For U/2S ; 1, both midlatitude and low-latitude cy-

clones form. The formation of the low-latitude cyclone

appears to be roughly independent of the midlatitude

cyclone. It results from an alteration of the basic state by

FIG. 14. Tropopause maps as in Fig. 12, but from simulations with initial temperature reduced by 5 K: (a) S15_U30_C,

240 h and (b) S15_U40_C, 264 h.


convection that, in turn, results from thermodynamic

destabilization of the troposphere to moist convection

where surface moisture fluxes are strongest. The basic

state modified by convection supports moist baroclinic

instability that manifests itself as a subtropical cyclone

growing with a minimum of surface baroclinicity in the

presence of deep westerly vertical wind shear. This evo-

lution, summarized in the schema in the right column

FIG. 15. SLP (CI 5 4 hPa), relative vorticity at 900 hPa (color shaded), and uTR (thick gray lines) for simulations initialized with a

40 m s21 jet with normal mode amplitude set to 0.001 K; (a),(d) Kain–Fritsch cumulus scheme (same as previously discussed simulations

at 228 and 276 h, respectively); (b),(e) grid spacing of 25 km, still with the Kain–Fritsch scheme, at 372 and 420 h, respectively; and (c),(f)

Grell–Devenyi scheme with a grid spacing of 50 km at 372 and 420 h, respectively.


of Fig. 16, resembles qualitatively that discussed by

Montgomery and Farrell (1993), but here the basic state

and the perturbations evolve rather than being prescribed.

Whether the subtropical cyclone becomes a dominant

midlatitude system depends on the relative rates of

growth of the midlatitude and subtropical systems and

their spatial phase relation with each other. While it

appears that there is often competition between sub-

tropical and midlatitude systems, there are instances in

which the subtropical cyclone moves into midlatitudes

as a strong cyclone. This situation is similar to the variety

of cyclone outcomes possible in extratropical transition.

We devised a metric that describes the relative PV

contributions from near-surface baroclinicity (PV1) and

cyclonic PV in the lower and middle troposphere (PV2).

For U/2S� 1, all cyclones originate with PV1 * PV2 and

are therefore primarily of baroclinic origin. For U/2S ; 1,

cyclones originate at low latitudes and are characterized

by PV1/PV2� 1 initially. They form in the presence of

moderate westerly shear and synoptic-scale disturbances

of modest amplitude. These waves initiate as Rossby

waves on the subtropical dynamic tropopause. They de-

stabilize the troposphere and organize deep, moist con-

vection from which the surface cyclone grows. We

identify this class of cyclones as subtropical cyclones in

a dynamical, rather than geographical, sense. They are

distinguished from secondary cyclones such as frontal

cyclones (Thorncroft and Hoskins 1990) and real-world

cyclones such as kona lows by the near absence of sur-

face baroclinicity. Yet, the formation of subtropical cy-

clones fundamentally requires deep vertical wind shear

and quasigeostrophic dynamics. In this way, subtropical

FIG. 16. Schema representing two idealized development pathways. Each panel depicts the axis of either the

extratropical or subtropical jet stream (heavy solid line with arrow), the position of major surface cyclones (L’s), and

cold and warm fronts. Large L’s indicate mature cyclones; small L’s indicate incipient cyclones.


cyclones are also distinct from the majority of tropical

cyclones forming in the deep tropics. In their mature

stage, subtropical cyclones may evolve into either bar-

oclinic or tropical cyclones.

Subtropical cyclones, by our definition, belong to a

general class of previously identified cyclonic distur-

bances in which the principal agent of development is

condensation heating, but where there is a guiding, bar-

oclinic structure that organizes the heating. Such related

disturbances include mesoscale convective vortices initi-

ated and modulated by weak baroclinic waves, diabatic

Rossby vortices, and possibly many instances of high-

latitude cyclones over warm water such as polar lows and

Mediterranean cyclones. It is possible that all such cyclonic

systems are manifestations of a similar set of dynamics.

The present paper has not addressed the formation of

tropical cyclones from subtropical cyclones. Part of this

is because we do not have the model resolution to prop-

erly form the inner core structure that characterizes

a tropical cyclone. However, it is worth noting that many

previous studies have shown that tropical cyclones do

form from subtropical cyclones and occasionally from

secondary cyclones, with the terms ‘‘subtropical’’ and

‘‘secondary’’ following the above definitions. The final

schematic of Fig. 16 suggests the possibility of a ‘‘tropi-

cal transition’’ (Davis and Bosart 2004) occurring on the

east side of the cyclonic filament of PV at low latitudes.

While the basic knowledge of the nature of sub-

tropical cyclones and their behavior gleaned from our

simulations appears internally consistent and consistent

with the modest amount of literature on the topic, some

words of caution are probably worthwhile. First, we

have barely begun to explore the parameter space of this

moist baroclinic dynamics problem. It would be useful to

perform experiments that attempt to separate the de-

stabilization effects from moisture fluxes induced by the

imposed surface winds from the effects of barotropic

shear. Furthermore, the transition of secondary and

subtropical cyclones to tropical cyclones needs to be

thoroughly investigated in order to provide the topic of

tropical transition with a more theoretical context.

Acknowledgments. The author is indebted to Riwal

Plougenvan of LMD Paris for providing the code and

scripts that modified the WRF baroclinic wave test case

for more general applications. The paper also benefitted

from discussions with Rich Rotunno of NCAR.

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